How does Anselm's ontological argument in Proslogion try to prove God's existence?

In his Proslogion, St. Anselm of Canterbury presents the ontological argument to prove God's existence through reason alone, rather than relying on scriptural authority.12

The argument begins with the definition of God as "that than which nothing greater can be conceived" (aliquid quo nihil majus cogitari possit). Anselm posits that even a person who denies God’s existence understands this concept, meaning the idea exists within their intellect.3412

He then argues that it is greater to exist in both reality and the understanding than to exist in the understanding alone. If the being defined as the greatest possible were to exist only in the mind, one could conceive of an even greater being—one that also exists in reality. Therefore, to avoid a logical contradiction, the unsurpassably perfect being must necessarily exist in reality.1234

While historically significant, this argument has been widely contested by philosophers such as Immanuel Kant, who argued that existence is not a predicate that can be added to a concept to define its perfection.4